MinT - Best Known (12−6, 12, s)-Nets in Base 9

Best Known (12−6, 12, s)-Nets in Base 9

(12−6, 12, 164)-Net over F₉ — Constructive and digital

Digital (6, 12, 164)-net over F₉, using

trace code for nets [i] based on digital (0, 6, 82)-net over F₈₁, using
- net from sequence [i] based on digital (0, 81)-sequence over F₈₁, using
  - generalized Faure sequence [i]
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 0 and N(F) ≥ 82, using
    - the rational function field F₈₁(x) [i]
  - Niederreiter sequence [i]

(12−6, 12, 1488)-Net in Base 9 — Upper bound on s

There is no (6, 12, 1489)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 282491 209817 > 9¹² [i]